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Math Help - Complex Conjugation Vector Space

  1. #1
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    Complex Conjugation Vector Space

    Can someone help me with this vector proof?

    Let V be the set of all complex-valued functions f on the real line such that (for all t in R)
    f(-t)=f(t) bar (the bar denotes complex conjugation)
    Show that V, with the operations
    (f+g)(t) = f(t) + g(t)
    (cf)(t) = cf(t)

    is a vector space over the field of real numbers.
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  2. #2
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    Quote Originally Posted by krepka View Post
    Can someone help me with this vector proof?

    Let V be the set of all complex-valued functions f on the real line such that (for all t in R)
    f(-t)=f(t) bar (the bar denotes complex conjugation)
    Show that V, with the operations
    (f+g)(t) = f(t) + g(t)
    (cf)(t) = cf(t)

    is a vector space over the field of real numbers.
    You basically need to show that if f_1,f_2 \in V \implies f_1+f_2 \in V and cf_1\in V.
    Just follow the definitions here.
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